Well, yeah, authoritarian (Leninist-Stalinist) Communist regimes weren't particularly eager to highlight that Leninist vanguardism was a sharp repudiation of central elements of Marxist Communism (and one that, after making some early marks, was singularly unsuccessful in establishing itself any place where capitalism and the elements Marx saw as necessary for moving on to socialism had ever existed, as opposed to other strands of socialism, both Marxist-derived and otherwise), and that Marxist Communism itself was one of many strands of socialist theory, and that all of the advanced "capitalist" economies of the West had -- largely as a result of non-Marxist, or at least non-Leninist, socialist forces -- long since departed from the "capitalism" critiqued by Marx for what the modern mixed economy, which is neither strictly capitalist nor socialist by 19th or early 20th century standards, keeping superficially the property structure of the former, with many structures inspired by the latter.
> I think "communism is different than socialism" is a Western-countries' thing
Well, yes, seeing socialism as broader than Communism is probably more common in places where the successful forms of socialism absolutely weren't Leninist Communism, often weren't other derivations of Marxist Communism -- and, in some cases, characterized Leninist Communist as "state capitalism" -- and had to deal with domestic opponents that wanted to paint them with the brush of Leninism-Stalinism and its atrocities than in one-party Leninist-Stalinist states.
I was born in the Socialist Republic of Romania (https://en.wikipedia.org/wiki/Socialist_Republic_of_Romania) in the early 1980s, which was ruled by the Romanian Communist Party (which was the only allowed party). The situation was pretty much the same in all the former Eastern Block countries, with socialism being used interchangeably with communism, there were no debates in our local press about which one was which. I think "communism is different than socialism" is a Western-countries' thing, where Obama is called a socialist because he tried to make sense of the US health-care system (long story short: he's not).
And on a more general level of discussion, I'm not sure there really is a difference between the two. I've read some left-leaning literature (Marx's Capital I, his "German Ideology" and other younger writings of his, Lenin's "What Is to Be Done?", Kołakowski's 3-volume "Main Currents of Marxism", some Lukács, Jacques Rancière's "Nights of Labor: The Workers Dream in Nineteenth Century France") and no-where in those volumes there was a clear distinction made between "communism" and "socialism". The only nuance I can think of is Lenin's insistence that trade-unionist communism was a bad thing, because that involved making a pact with the "enemy" (the capitalists) and only settling for small gains, ignoring the bigger picture. He was of course right, from a workers' point of view perspective, you either control all means of productions or you risk still depending on the capitalists. 100+ or so years since his early writings the European working class is basically dead.